According to TMZ, Za was in Bieber's Calabasas backyard Thursday ... spray painting his demand to free Bieber and Khalil after their arrests in Miami Beach early that morning.

Now here's what's really interesting. People familiar with the skateboard ramp pointed TMZ in the direction of the splatter marks. Sources VERY familiar with the situation tell TMZ ... they're EGG splatters.

TMZ reports that the splatters are highly relevant in the case of the egging of Bieber's neighbor last week. One connected source told TMZ ... Bieber and his buds were stoned in his backyard just before the egging incident, throwing eggs at each other and hitting the ramp. Then on a lark they went next door and did the same to Justin's neighbor.

A key law enforcement source tells TMZ ... when Sheriff's deputies executed their search warrant last week ... they saw the skate ramp from a distance but didn't scrutinize it.

The law enforcement source said to TMZ ... this makes total sense ... because they were all baffled as to why Justin would suddenly attack the neighbor for no apparent reason. It makes more sense that the games in the backyard escalated to an egg attack on Justin's neighbor.